Discovering Physical Structure with Shallow Universal Polynomial Networks
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Shallow Universal Polynomial Networks (SUPNs) have recently shown great promise to combine the historic strengths of polynomial approximation with the flexibility of neural networks for interpretable, efficient surrogate models. In particular, on a suite of test problems, SUPN error is an order of magnitude lower than polynomials on nonsmooth functions, and several orders of magnitude lower than feedforward networks on smooth functions. Furthermore, SUPNs exhibit significantly more robustness to network initialization than other networks. However, their utility in physical settings governed by partial differential equations remains unexplored. In this talk, we use a SUPN as a physics-informed neural network and the trunk in a Deep Operator Network. Our results show competitive accuracy and reduced uncertainty compared to a neural-network baseline.
